Shift current response in twisted double bilayer graphenes

TL;DR

The paper addresses how the shift current, a second-order nonlinear optical response, behaves in twisted double bilayer graphene (TDBG) as a function of twist angle $\theta$, vertical bias $\Delta$, and carrier density, using a perturbative, velocity-gauge framework on an effective continuum Hamiltonian. It compares AB-AB and AB-BA stackings, showing strong low-frequency enhancement as $\theta$ decreases (smaller moiré gaps) and a systematic sign reversal between the two variants under large $\Delta$, with insights drawn from AB-stacked bilayer graphene. The reversal originates from the relative 180° rotation of one bilayer and persists when moiré coupling is included, indicating a symmetry-driven control of nonlinear response. Overall, the results highlight moiré engineering as a means to tailor shift current in graphene-based heterostructures with potential optoelectronic applications, especially at small twist angles and finite vertical bias.

Abstract

We calculate the shift current response in twisted double bilayer graphenes (TDBG) by applying the perturbative approach to the effective continuum Hamiltonian. We have performed a systematic study of the shift current in AB-AB and AB-BA stacked TDBG, where we have investigated the dependence of the signal on the twist angle, the vertical bias voltage and the Fermi level. The numerical analyses demonstrate that the signal is greatly enhanced as the twist angle is reduced. Notably, we also found that there is a systematic sign reversal of the signal in the two stacking configurations below the charge neutrality point for large bias voltages. We qualitatively explain the origin of this sign reversal by studying the shift current response in AB-stacked bilayer graphene.

Figures (9)

• Figure 1: (a) We show a schematic diagram of AB-stacked BLG and the stacking configuration in AB-AB stacked TDBG on the top. The corresponding moiré pattern is shown in the bottom. In (b), we shows the same diagrams, but for AB-BA stacked TDBG, where the blue bilayer gains a $180^\circ$ offset.
• Figure 2: (a) The band structures of AB-AB stacked TDBG and density plots of $\sigma^x_{xx}(\omega;E_{\rm{F}})$ signal for various twist angles. Here, we used $\theta=0.4^\circ, 0.8^\circ, 1.4^\circ, 2.0^\circ$ and $3.0^\circ$. (b) The corresponding plots for the $\sigma^y_{yy}(\omega;E_{\rm{F}})$ signal in the AB-BA variant. We note that the $\sigma^y_{yy}$/$\sigma^x_{xx}$ component vanishes due to the $C_{2x}$/$C_{2y}$ symmetry in the AB-AB/AB-BA variant. The moiré Brillouin zone in shown in the top right corner.
• Figure 3: The band structures and $\sigma^x_{xx}(\omega;E_{\rm{F}})$ density plots of (a) AB-AB and (b) AB-BA stacked TDBG for various strengths of the vertical bias voltage $\Delta$. Here, we used $\Delta=$ 0, 10, 20 and 50 meV. The grey arrows indicate the respective charge neutral gaps.
• Figure 4: The band structures and $\sigma^y_{yy}(\omega;E_{\rm{F}})$ density plots of (a) AB-AB and (b) AB-BA stacked TDBG for various strengths of the vertical bias voltage $\Delta$. Here, we used $\Delta=$ 0, 10, 20 and 50 meV. The grey arrows indicate the respective charge neutral gaps.
• Figure 5: A close-up view of the $\sigma^x_{xx}$/$\sigma^y_{yy}$ responses in (a)/(c) AB-AB and (b)/(d) AB-BA TDBG shown in Fig. \ref{['fig:3-tdbg0800-50xxx']} and \ref{['fig:3-tdbg0800-50yyy']}. We have labelled regions where a sign reversal between the two stacking configurations can be seen.